Lesson 7.4 Day 2 Mixture and wind/current problems
Question #1 MIXTURE
One antifreeze solution is 10% alcohol. Another is 18% alcohol. How many liters of each antifreeze
solution should be combined to create 20 liters of antifreeze solution that is 15% alcohol?
Common sense. Since my final solution is 15%, there should be more of the 18% solution than the 10%
solution. Think about why.
Lets define some variables
Let x = liters of 10 % solution
Let y = liters of 18% solution
Since I want a total of 20 liters of solution. My first equation will just sum this up
X + Y = 20
My second equation will deal with the %’s. It is similar to the second equation of coin problems. I need
to multiply my % as a decimal and the amount of each solution.
.10X +.18Y = (.15)(20)
***make sure you multiply the percent of final solution by the total # of liters
(this is the part that most people forget)
Multiply the .15 and 20 in the second equation to get 3
Multiply the second equation by 100 to get rid of decimals
Multiply the first equation by -10 so the x’s will be eliminated.
Add my equations and solve for y. Substitute y into original and solve
for x. Check to see if your answer makes sense.
Question # 2 Wind/current problem. The first thing that you need to remember is that Distance =
Rate * Time
You may have to solve some problems for the rate before you can solve for what is being asked.
Suppose it takes you and a friend 3.2 hours to canoe 12 miles downstream ( with the current). During
the return trip, it takes you and your friend 4.8 hours to paddle upstream ( against the current) to the
original starting point. Find the average paddling speed in still water of you and your friend and the
average speed of the current of the river. Round answers to the nearest tenth.
Wow Did you understand all of that? If not read on.
Lets start with a D=R*T chart.
So now we have our chart complete. Our rate downstream is 3.75 and upstream 2.5
Lets talk about our rates.
When we are going downstream, our rate is our boat speed + current.
When we are going upstream, our rate is our boat speed – current.
Make sense?
Continued on next page.
if you read this problem, let me know tomorrow.
Lets define some variables for the boat speed and the current
B= boat speed
Downstream
Up stream
c = current
3.75 = B + c
2.5 = B – c
6.25 = 2B
Since the C’s can be eliminated I just added the equations
Solve for B
3.125 = B
Then 3.75 = 3.125 + c
Substitute in to solve for c.
.625 = C
B= 3.1
C = .6
Round only at the end. Never in the middle of a problem or your answer will be off.